Managing Epistemic Uncertainty in Design Models through Type-2 Fuzzy Logic Multidisciplinary Optimization

Humans have a natural ability to operate in dynamic environments and perform complex tasks with little perceived effort. An experienced ship designer can intuitively understand the general consequences of design choices and the general attributes of a good vessel. A person's knowledge is often ill-structured, subjective, and imprecise, but still incredibly effective at capturing general patterns of the real-world or of a design space. Computers on the other hand, can rapidly perform a large number of precise computations using well-structured, objective mathematical models, providing detailed analyses and formal evaluations of a specfic set of design candidates. In ship design, which involves generating knowledge for decision-making through time, engineers interactively use their own mental models and information gathered from computer-based optimization tools to make decisions which steer a vessel's design. In recent decades, the belief that large synthesis codes can help achieve cutting-edge ship performance has led to an increased popularity of optimization methods, potentially leading to rewarding results. And while optimization has proven fruitful to structural engineering and the aerospace industry, its applicability to early-stage design is more limited for three main reasons. First, mathematical models are by definition a reduction which cannot properly describe all aspects of the ship design problem. Second, in multidisciplinary optimization, a low-fidelity model may incorrectly drive a design, biasing the system level solution. Finally, early-stage design is plagued with limited information, limiting the designer's ability to develop models to inform decisions. This research extends previously done work by incorporating type-2 fuzzy logic into a human-centric multidisciplinary optimization framework. The original framework used type-1 fuzzy logic to incorporate human expertise into optimization models through linguistic variables. However, a type-1 system does not properly account for the uncertainty associated with linguistic terms, and thus does not properly represent the uncertainty associated with a human mental model. This limitation is corrected with the type-2 fuzzy logic multidisciplinary optimization presented in this work, which more accurately models a designer's ability to "communicate, reason and make rational decisions in an environment of imprecision, uncertainty, incompleteness of information and partiality of truth" (Mendel et al., 2010). It uses fuzzy definitions of linguistic variables and rule banks to incorporate "human intelligence" into design models, and better handles the linguistic uncertainty inherent to human knowledge and communication. A general mathematical optimization proof of concept and a planing craft case study are presented in this dissertation to show how mathematical models can be enhanced by incorporating expert opinion into them. Additionally, the planing craft case study shows how human mental models can be leveraged to quickly estimate plausible values of ship parameters when no model exists, increasing the designer's ability to run optimization methods when information is limited.PHDNaval Architecture & Marine EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145891/1/doriancb_1.pd

Study of the dependencies between in-service degradation and key design parameters with uncertainty for mechanical components.

The design features of machine components can impact significantly in its life while in-service, and only relatively few studies which are case specific have been undertaken with respect to this. Hence, the need for more understanding of the influence of geometric design features on the service life of a machine component. The aim of this research is to develop a methodology to assess the degradation life of a mechanical component due to geometric design influence in the presence of uncertainties and its application for the optimisation of the component in the presence of these uncertainties. This thesis has proposed a novel methodology for assessing the thermal fatigue life, a degradation mechanism based on the influence of design features in the presence of uncertainties. In this research a novel uncertainty analysis methodology that is able to handle simultaneously the presence of aleatory and epistemic uncertainties is proposed for a more realistic prediction and assessment of a components thermal fatigue degradation life estimated using finite element analysis. A design optimisation method for optimising the components design in the presence of mixed uncertainty, aleatory and epistemic uncertainties is also proposed and developed. The performance of the proposed methodology is analysed through the use of passenger vehicle brake discs. The novel uncertainty quantification methodology was initially applied on a solid brake disc, and validated for generalisability using a vented brake disc which has more complex design features. While the optimisation method as proposed was applied on the vented brake disc. With these this research proposes a validated set of uncertainty and optimisation methodology in the presence of mixed uncertainties for a design problem. The methodologies proposed in this research provide design engineers with a methodology to design components that are robust by giving the design with the least uncertainty in its output as result of design parameters inherent variability while simultaneously providing the design with the least uncertainty in estimation of its life as a result of the use of surrogate models.PhD in Manufacturin

An EA-based approach to design optimization using evidence theory

For problems involving uncertainties in design variables and parameters, a bi-objective evolutionary algorithm (EA) based approach to design optimization using evidence theory is proposed and implemented in this paper. In addition to a functional objective, a plausibility measure of failure of constraint satisfaction is minimized. Despite some interests in classical optimization literature, such a consideration in EA is rare. Due to EA's flexibility in its operators, non-requirement of any gradient, its ability to handle multiple conflicting objectives, and ease of parallelization, evidence-based design optimization using an EA is promising. Results on a test problem and a couple of engineering design problems show that the modified evolutionary multi-objective optimization (EMO) algorithm is capable of finding a widely distributed trade-off frontier showing different optimal solutions corresponding to different levels of plausibility failure limits. Furthermore, a single-objective evidence based EA is found to produce better optimal solutions than a previously reported classical optimization procedure. Handling uncertainties of different types are getting increasingly popular in applied optimization studies and more such studies using EAs will make EAs more useful and pragmatic in practical optimization problem-solving tasks